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I want to whow that

$$ 2 \int_{\partial B} ( \nabla g) (x+ tz) z dz = 3t \int_{B} ( \Delta g)(x+tz) dz $$ Here, $ B$ is a unit sphere in $R^3$.

$$ x = (x_1, x_2, x_3), t \geqslant 0 $$ $$ \nabla = \left ( \frac{\partial}{\partial x_1}, \frac{\partial}{\partial x_2} , \frac{\partial}{\partial x_3} \right) $$ $$ \Delta = \sum_{j=1}^3 \frac{\partial^2}{\partial x_j^2} $$

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